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1	Interpolation of non-smooth functions on anisotropic finite element meshes Apel, Th. 30 October 1998 (has links) (PDF) In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang (Math. Comp. 54(1990)190, 483--493) are discussed. The modified operators are defined for non-smooth functions and are suited for the application on anisotropic meshes. The anisotropy of the elements is reflected in the local stability and approximation error estimates. As an application, an example is considered where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges. anisotropic weighted Sobolev spaces local interpolation error estimates. MSC 35A40 MSC 35J05 MSC 65N30 MSC 35B65 ddc:510
2	Elliptic problems in domains with edges: anisotropic regularity and anisotropic finite element meshes Apel, T., Nicaise, S. 30 October 1998 (has links) (PDF) This paper is concerned with the anisotropic singular behaviour of the solution of elliptic boundary value problems near edges. The paper deals first with the description of the analytic properties of the solution in newly defined, anisotropically weighted Sobolev spaces. The finite element method with anisotropic, graded meshes and piecewise linear shape functions is then investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates in anisotropically weighted spaces are derived. Moreover, it is shown that the condition number of the stiffness matrix is not affected by the mesh grading. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones. anisotropic weighted Sobolev spaces local interpolation error estimates MSC 35A40 MSC 35J05 MSC 65N30 MSC 35B65 ddc:510
3	A parallel version of the preconditioned conjugate gradient method for boundary element equations Pester, M., Rjasanow, S. 30 October 1998 (has links) (PDF) The parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two-dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems. conjugate gradient algorithm fast Fourier transform preconditioning numerical experiments Galerkin boundary element method Laplace equation parallelization MSC 65N38 MSC 65F10 MSC 65Y05 MSC 65F35 MSC 35J05 ddc:510
4	Realization and comparison of various mesh refinement strategies near edges Apel, T., Milde, F. 30 October 1998 (has links) (PDF) This paper is concerned with mesh refinement techniques for treating elliptic boundary value problems in domains with re- entrant edges and corners, and focuses on numerical experiments. After a section about the model problem and discretization strategies, their realization in the experimental code FEMPS3D is described. For two representative examples the numerically determined error norms are recorded, and various mesh refinement strategies are compared. singularities near edges Fichera corner finite element methods convergence a priori mesh grading algorithms adaptive mesh refinement Poisson's equation MSC 65N50 MSC 65N30 MSC 35J05 ddc:510
5	Elliptic problems in domains with edges: anisotropic regularity and anisotropic finite element meshes Apel, T., Nicaise, S. 30 October 1998 (has links) This paper is concerned with the anisotropic singular behaviour of the solution of elliptic boundary value problems near edges. The paper deals first with the description of the analytic properties of the solution in newly defined, anisotropically weighted Sobolev spaces. The finite element method with anisotropic, graded meshes and piecewise linear shape functions is then investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates in anisotropically weighted spaces are derived. Moreover, it is shown that the condition number of the stiffness matrix is not affected by the mesh grading. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones. info:eu-repo/classification/ddc/510 ddc:510
6	Interpolation of non-smooth functions on anisotropic finite element meshes Apel, Th. 30 October 1998 (has links) In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang (Math. Comp. 54(1990)190, 483--493) are discussed. The modified operators are defined for non-smooth functions and are suited for the application on anisotropic meshes. The anisotropy of the elements is reflected in the local stability and approximation error estimates. As an application, an example is considered where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges. info:eu-repo/classification/ddc/510 ddc:510 anisotropic weighted Sobolev spaces local interpolation error,estimates. MSC 35A40 MSC 35J05 MSC 65N30 MSC 35B65
7	A parallel version of the preconditioned conjugate gradient method for boundary element equations Pester, M., Rjasanow, S. 30 October 1998 (has links) The parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two-dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems. info:eu-repo/classification/ddc/510 ddc:510 conjugate gradient algorithm fast Fourier transform preconditioning numerical experiments Galerkin boundary element method Laplace equation parallelization MSC 65N38 MSC 65F10 MSC 65Y05 MSC 65F35 MSC 35J05
8	Realization and comparison of various mesh refinement strategies near edges Apel, T., Milde, F. 30 October 1998 (has links) This paper is concerned with mesh refinement techniques for treating elliptic boundary value problems in domains with re- entrant edges and corners, and focuses on numerical experiments. After a section about the model problem and discretization strategies, their realization in the experimental code FEMPS3D is described. For two representative examples the numerically determined error norms are recorded, and various mesh refinement strategies are compared. info:eu-repo/classification/ddc/510 ddc:510 MSC 65N50, MSC 65N30, MSC 35J05

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